A new improvement of Hölder inequality via isotonic linear functionals

İmdat İşcan; İmdat İşcan

doi:10.3934/math.2020116

AIMS Mathematics

2020, Volume 5, Issue 3: 1720-1728. doi: 10.3934/math.2020116

Previous Article Next Article

Research article

A new improvement of Hölder inequality via isotonic linear functionals

İmdat İşcan ^,

Department of Mathematics, Faculty of Arts and Sciences, Giresun University, 28200, Giresun-Turkey

Received: 30 October 2019 Accepted: 07 February 2020 Published: 13 February 2020
MSC : 26A51, 26D15

In this paper, a new improvement of celebrated Hölder inequality using isotonic linear functionals is established. An important feature of the new inequality obtained here is that many existing inequalities related to the Hölder inequality can be improved which we also illustrate with an application.
- Hölder inequality,
- Young inequality,
- integral inequalities,
- Hermite-Hadamard type inequality
Citation: İmdat İşcan. A new improvement of Hölder inequality via isotonic linear functionals[J]. AIMS Mathematics, 2020, 5(3): 1720-1728. doi: 10.3934/math.2020116

Related Papers:

Abstract

In this paper, a new improvement of celebrated Hölder inequality using isotonic linear functionals is established. An important feature of the new inequality obtained here is that many existing inequalities related to the Hölder inequality can be improved which we also illustrate with an application.

References

[1]	S. Abramovich, J. E. Pečarić, S. Varošanec, Sharpening Hölder's and Popoviciu's inequalities via functionals, The Rocky Mountain Journal of Mathematics, 34 (2004), 793-810. doi: 10.1216/rmjm/1181069827
[2]	L. Ciurdariu, Some refinements of Hölder's inequalities via isotonic linear functionals, Journal of Science and Arts, 14 (2014), 221-228.
[3]	L. Ciurdariu, Several Applications of Young-Type and Holder's Inequalities, Applied Mathematical Sciences, 10 (2016), 1763-1774. doi: 10.12988/ams.2016.6275
[4]	S. S. Dragomir, A Grüss type inequality for isotonic linear functionals and applications, Demonstratio Mathematica, 36 (2003), 551-562.
[5]	S. S. Dragomir, Some results for isotonic functionals via an inequality due to Kittaneh and Manasrah, Fasciculi Mathematici, 59 (2017), 29-42. doi: 10.1515/fascmath-2017-0015
[6]	S. S. Dragomir, M. A. Khan, A. Abathun, Refinement of the Jensen integral inequality, Open Mathematics, 14 (2016), 221-228.
[7]	A. Guessab, O. Nouisser, J. Pečarić, A multivariate extension of an inequality of BrennerAlzer, Archiv der Mathematik, 98 (2012), 277-287. doi: 10.1007/s00013-012-0361-7
[8]	A. Guessab, G. Schmeisser, Sharp Integral Inequalities of the HermiteHadamard Type, J. Approx. Theory, 115 (2002), 260-288. doi: 10.1006/jath.2001.3658
[9]	A. Guessab, G. Schmeisser, Convexity results and sharp error estimates in approximate multivariate integration, Math. Comput. Mathematics of computation, 73 (2004), 1365-1384.
[10]	İ. İşcan, New Refinements for integral and sum forms of Hölder inequality, J. Inequal. Appl., 2019 (2019), 1-11. doi: 10.1186/s13660-019-1955-4
[11]	D. S. Mitrinović, J. E. Pečarić, A. M. Fink. Classical and new inequalities in analysis, KluwerAkademic Publishers, Dordrecht, Boston, London, 1993.
[12]	J. E. Pečarić, Generalization of the power means and their inequalities, Journal of Mathematical Analysis and Applications, 161 (1991), 395-404. doi: 10.1016/0022-247X(91)90339-2
[13]	J. E. Pečarić, F. Proschan Y. L. Tong, Convex functions, partial orderings and statistical applications, Academic Press, New York, 1992.
[14]	M. Z. Sarıkaya, E. Set, M. E. Özdemir, New Some Hadamard's Type Inequalities for Co-ordinated Convex Functions, Tamsui Oxford Journal of Information and Mathematical Sciences, 28 (2012), 137-152.

Reader Comments

Your name:*

Email:*
© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)